We don't need a royal family and I personally think the country would be a lot better without it. They encourage people to be politically apathetic, misty-eyed and nostalgic about the country when, really, there's a lot that needs fixing.
They may remind us of our history, but they also represent all that is bad about the history of our country: the richest constantly taking advantage of the poor, a small minority of individuals enjoying unearned wealth and privilege, secretive networks of unelected old boys' clubs with far too much political influence and the repugnant class system.
The Queen has far more political power and influence than people are aware of. I expect people would feel less benevolent towards her if the actual level of her interference in politics was public knowledge.
Republics may seem "boring" to some people, but the people lucky enough to live in these countries enjoy far better rights (like actual having their rights actually enshrined in written constitutions) and are far more engaged in politics. They also have higher voting turnouts.
You always hear the argument "I don't want a president Blair/Brown/Cameron etc.", implying that the only alternative to having a monarchy is a US-style political system, completely ignoring the political systems of our closest neighbours like the Republic of Ireland, which has a ceremonial head of state in its president.